Param Himalaya - परम हिमालय

Lenz's Law The polarity of induced e.m.f in a closed circuit or coil is such that it oppose the cause which produces it. Faraday 's law of electromagnetic induction, induced e.m.f. in a closed circuit is given by :  $E= -N \frac{d\Phi_B}{dt}$ Where:  * \mathcal{E} is the induced EMF  * N is the number of turns in the coil  * \frac{d\Phi_B}{dt} is the rate of change of magnetic flux through the coil * Negative sign shows that induced e.m.f opposes the rate of change of magnetic flux in a closed circuit. Conservation of Energy Energy cannot be created or destroyed, but it can be transformed from one form to another within a closed system. The total amount of energy in an isolated system remains constant over time. The Relationship Between Lenz's Law and Conservation of Energy :  Consider a bar magnet moving towards a coil of wire.As the magnet approaches, the magnetic flux through the coil increases. According to Lenz's Law, the induced current in the coil will cr...

Mutual Inductance of Two Long Co-axial Solenoids of Equal Length Consider two solenoids $S_1$ and $S_2$ such that the solenoid $S_2$ completely surrounds the solenoid $S_1$. Let length of each solenoid be $l$, and the area of cross-section of each solenoid is $A$. Let $N_1$ and $N_2$ be the total number of turns of solenoid $S_1$ and $S_2$ respectively. $\therefore$ Number of turns per unit length of solenoid $S_1$ is given by, $n_1 = \frac{N_1}{l}$. Number of turns per unit length of solenoid $S_2$ is given by, $n_2 = \frac{N_2}{l}$. Let current $I_1$ flow through solenoid $S_1$. Then magnetic field inside the solenoid $S_1$ is given by, $ B_1 = \mu_0 n_1 I_1 = \mu_0 \frac{N_1}{l} I_1 $ Magnetic flux linked with each turn of solenoid $S_2$ is given by,  $d\phi_2 = B_1 A = \mu_0 \frac{N_1}{l} I_1 A$. Then, total magnetic flux linked with $N_2$ turns of the solenoid $S_2$ is given by $ \phi_2 = N_2 d\phi_2$ $ \phi_2= N_2 \mu_0 \frac{N_1}{l} I_1 A$ $ \phi_2= \mu_0 \frac{N_1 N_2}{l} A...

Coefficient of Mutual Induction or Mutual Inductance :  It is known that the magnetic flux linked with the secondary coil is directly proportional to the current flowing through the primary coil. i.e., $\phi_s \propto I_p$ or, $\phi_s = MI_p \quad \dots (1) $ where $M$ is a constant of proportionality called \textbf{co-efficient of mutual induction or Mutual inductance}. If $I_p = 1$, then $M = \phi_s$. Thus, magnetic inductance of two coils or circuits is defined as the magnetic flux linked with the secondary coil due to the flow of unit current in the primary coil. According to Faraday's law of electromagnetic induction, $ \varepsilon_s = - \frac{d\phi_s}{dt} $ Using equation (1), we get $ \varepsilon_s = - \frac{dMI_p}{dt}$ $ \varepsilon_s= -M \frac{dI_p}{dt} \quad \dots (3) $ or $ M = - \frac{\varepsilon_s}{\frac{dI_p}{dt}} \quad \dots (4) $ If $-\frac{dI_p}{dt} = 1$, then $M =\varepsilon_s$. Thus, mutual inductance of two coils can be defined as the induced e.m.f. produced in ...

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Derive an expression for self inductance of a solenoid. What happens to the self inductance of the coil if it is wound on a rod of magnetic material. State the factors on which the self inductance of a coil depends. Consider a long solenoid of length $l$, area of cross section $A$ and number of turns per unit length $n$. Let $I$ be the current flowing through the solenoid. The magnetic field inside this solenoid is uniform and given by $ B = \mu_0 n I $ Total number of turns in the solenoid, $N = nl$. Now the magnetic flux linked with each turn of the solenoid, $d\phi_B = B \times A = \mu_0 n I A$. Total magnetic flux linked with the whole solenoid, $ \phi_B = \text{magnetic flux linked with each turn} \times \text{number of turns in the solenoid} $ $ \phi_B = (\mu_0 n I A) \times (nl) = \mu_0 n^2 I Al \quad \dots (1) $ or $ \phi_B = LI \quad \dots (2) $ Also, From (1) and (2), we get $ LI = \mu_0 n^2 I Al $ or $ L = \mu_0 n^2 Al \quad \dots (3) $ Since $n = \frac{N}{l}$. Hence eqn. (3...

Definition of Inductance: Inductance is a fundamental property of an electrical conductor or circuit. It describes the tendency of the conductor to oppose any change in the electric current flowing through it. When the current flowing through a conductor changes, it creates a changing magnetic field around it. According to Faraday's Law of Induction and Lenz's Law, this changing magnetic field induces a voltage (electromotive force or EMF) across the conductor. This induced voltage acts in a direction that opposes the original change in current. In simpler terms: Inductance is like electrical inertia – it resists changes in current flow, just as mass resists changes in velocity. Quantitatively: It is defined as the ratio of the induced voltage (EMF) to the rate of change of current causing it:      E = -L (dI/dt)      Where:      E = induced voltage (EMF)      L = inductance      dI/dt = rate of change of current...

Define Self Inductance and Expression for Coefficient of It. Define Self Inductance :  Self-inductance is the property of a coil (or any conductor) to oppose a change in the current flowing through it by inducing an electromotive force (EMF) in itself.  This phenomenon arises due to Faraday's law of electromagnetic induction. When the current through the coil changes, the magnetic flux linked with the coil also changes, inducing an EMF that opposes this change in current. This induced EMF is also known as back EMF. Self inductance is also knowns as inertia of electricity. Coefficient of Self Induction or Self Inductance :  The magnetic field at any point due to a current carrying coil is directly proportional to the current. Therefore, the magnetic flux ($\phi_B = BA$) through the area bounded by the current carrying coil is directly proportional to the current flowing in the coil, i.e., $ \phi_B \propto I $ $ \phi_B = LI $ where $L$ is the constant of proportionality and...